A. The In-order traversal of any BST will always yield keys in a strictly increasing sorted order.
Answer: True The definition of a Binary Search Tree (BST) is that for any given node, all keys in its left subtree are smaller than the node's key, and all keys in its right subtree are larger. In-order traversal visits the left subtree, then the current node, then the right subtree. This process naturally visits all nodes in ascending order of their keys.
B. To find the minimum element in a non-empty BST, one must always traverse from the root to the leftmost leaf.
Answer: False While the minimum element is found by traversing left from the root as much as possible, the traversal ends at the leftmost node which may not necessarily be a leaf node if it has a right child. The minimum element is the node with no left child in the path from the root.
C. In a BST with N nodes, the post-order traversal can be uniquely determined if both the in-order and pre-order traversals are provided.
Answer: True Given any two of the three standard tree traversals (in-order, pre-order, post-order), the structure of the binary tree can be uniquely reconstructed, and thus the third traversal can also be uniquely determined.
D. If a BST is constructed by inserting keys in the order {1, 2, 3, 4, 5}, the resulting tree will have a height of 4 (where a single-node tree has height 0).
Answer: True Inserting the keys {1, 2, 3, 4, 5} sequentially results in a skewed tree (a linked list structure to the right): 1 becomes the root. 2 is inserted as the right child of 1. 3 is inserted as the right child of 2. 4 is inserted as the right child of 3. 5 is inserted as the right child of 4. The path from the root (1) to the deepest leaf (5) has 4 edges. Given the height definition (single-node tree height 0), the height is 4.
